The comments on Wednesday were some of William's first official remarks since the birth of his son on July 22.
William spoke on the island of Anglesey, Wales, where he attended an agricultural show, taking in a falconry display and talking with those in the crowd.
William compared the requirements of his job as a search and rescue helicopter pilot in northern Wales to the demands of being a new father.
"I have to say that I thought search and rescue duties over Snowdonia were physically and mentally demanding, but looking after a three-week-old baby is right up there."
William's wife, Kate, and Prince George were not at the show.
"This island has been our first home together, and will always be an immensely special place for us both," William said. "Catherine and I look forward to returning again and again over the coming years with our family."
William's appearance at the show is being considered as a farewell to the area where he and Kate have lived for several years in relative privacy. William's time as a rescue pilot based in Wales, where he has been based since 2009, is due to end next month. After that, he and his family are expected to move to London.Suggest a correction